The mathematics of risk sharing, with applications to Dutch pensions

Risk sharing is a basic notion both in finance and in insurance. When agents are exposed to different risks, it is possible that they can all improve their ex-ante utility by agreeing on a contract that will induce the ones who turn out to be lucky to provide compensation to those who do not come out so fortunate. It may not be so easy though to say when a system of risk sharing is to be considered "fair". The talk will discuss several models that can be used to answer this question. Applications will be given to highly stylized situations, but also to the intergenerational risk sharing that is implemented in the Dutch collective pension system. Mathematical disciplines that are touched upon include stochastic processes, control theory, convex analysis, and graph theory.

J.M. (Hans) Schumacher obtained the PhD degree in Mathematics from the Vrije Universiteit in Amsterdam in 1981. He held postdoc and visiting positions at the Laboratory for Information and Decision Systems of MIT, the Department of Econometrics of Erasmus University, Rotterdam, and the European Space Agency's research center ESTEC in Noordwijk, the Netherlands. In 1984 he joined the Centre for Mathematics and Computer Science (CWI) in Amsterdam, where his research was mainly focused on mathematical systems theory. In 1987 he was appointed to his current position as Professor of Mathematics at the Department of Econometrics and Operations Research of Tilburg University, first on a part-time basis, and since 1999 on a full-time basis. Hans Schumacher has served as corresponding editor of SIAM Journal on Control and Optimization, and he is Academic Director of the Executive Master of Actuarial Science (EMAS) program at TiasNimbas Business School. He is also affiliated with Netspar, the Dutch national network for studies on pensions, aging, and retirement.